(d^2-4d+4)y=x^2+e^x+cos^2(x)

Lösung

(d^{2} - 4 d + 4) y = x^{2} + e^{x} + cos^{2} (x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{2 x} \cdot \int - \frac{x ( x ^{2} + e ^{x} + cos ^{2} ( x ) )}{e ^{2 x}} d x + e^{2 x} x \cdot \int \frac{x ^{2} + e ^{x} + cos ^{2} ( x )}{e ^{2 x}} d x

Schritte zur Lösung

(d^{2} - 4 d + 4) y = x^{2} + e^{x} + cos^{2} (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{2 x} \cdot \int - \frac{x ( x ^{2} + e ^{x} + cos ^{2} ( x ) )}{e ^{2 x}} d x + e^{2 x} x \cdot \int \frac{x ^{2} + e ^{x} + cos ^{2} ( x )}{e ^{2 x}} d x

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{2 x} \cdot \int - \frac{x ( x ^{2} + e ^{x} + cos ^{2} ( x ) )}{e ^{2 x}} d x + e^{2 x} x \cdot \int \frac{x ^{2} + e ^{x} + cos ^{2} ( x )}{e ^{2 x}} d x

y^{^{''}} + 4 y^{^{'}} = sin^{3} (x)

(d - 1)^{2} (d^{2} + 1) y = 3 x^{2} - 5 x + 2

y^{^{''}} - 4 y = (x^{2} - 4) sin (2 x)

(d^{2} - 13 d + 12) y = 2008

(d^{2} + 9) y = sec (3 x)